145,986 research outputs found

    Design &implementation of complex-valued FIR digital filters with application to migration of seismic data

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    One-dimensional (I-D) and two-dimensional (2-D) frequency-space seismic migration FIR digital filter coefficients are of complex values when such filters require special space domain as well as wavenumber domain characteristics. In this thesis, such FIR digital filters are designed using Vector Space Projection Methods (VSPMs), which can satisfy the desired predefined filters' properties, for 2-D and three-dimensional (3-D) seismic data sets, respectively. More precisely, the pure and the relaxed projection algorithms, which are part of the VSPM theory, are derived. Simulation results show that the relaxed version of the pure algorithm can introduce significant savings in terms of the number of iterations required. Also, due to some undesirable background artifacts on migrated sections, a modified version of the pure algorithm was used to eliminate such effects. This modification has also led to a significant reduction in the number of computations when compared to both the pure and relaxed algorithms. We further propose a generalization of the l-D (real/complex-valued) pure algorithm to multi-dimensional (m-D) complex-valued FIR digital filters, where the resulting frequency responses possess an approximate equiripple nature. Superior designs are obtained when compared with other previously reported methods. In addition, we also propose a new scheme for implementing the predesigned 2-D migration FIR filters. This realization is based on Singular Value Decomposition (SVD). Unlike the existing realization methods which are used for this geophysical application, this cheap realization via SVD, compared with the true 2-D convolution, results in satisfactory wavenumber responses. Finally, an application to seismic migration of 2-D and 3-D synthetic sections is shown to confirm our theoretical conclusions. The proposed resulting migration FIR filters are applied also to the challenging SEGIEAGE Salt model data. The migrated section (image) outperformed images obtained using other FIR filters and with other standard migration techniques where difficult structures contained in such a challenging model are imaged clearly

    COMPLEX DIGITAL SIGNAL PROCESSING USING QUADRATIC RESIDUE NUMBER SYSTEMS.

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    This work presents the development of complex digital signal processing algorithms using number theoretic techniques. Residue number principles and techniques are applied to process complex signal information in Finite Impulse Response (FIR) and Infinite Impulse Response (IIR) digital filters. Residue coding of complex samples and arithmetic for processing complex data have been presented using principles of quadratic residues in the Residue Number System (RNS). In this work, we have presented modifications to the Quadratic Residue Number System (QRNS), which we have termed the Modified Quadratic Residue Number System (MQRNS), to process complex integers. New results and theorems have been obtained for the selection of operators to code complex integers into the new MQRNS representation. A novel scheme for residue to binary conversion has been presented for implementation using both the QRNS and MQRNS. Hardware implementations of multiplication intensive complex nonrecursive and recursive digital filters have been presented where the QRNS and MQRNS structures are realized using a bit-slice architectural approach. The computation of Complex Number Theoretic Transforms (CNTTs) and the hardware implementation of a radix-2 NTT butterfly structure, using high density ROM arrays, are presented in both the QRNS and MQRNS systems. As an illustration, the computation of the CNTT developed in this work, is used to compute Cyclic Convolution for complex sequences. These results are verified by computer programs. The recursive FIR filter structure for uniformly spaced frequency samples on the unit circle developed by adapting the Complex Number Theoretic z-transform, has been implemented using the QRNS and MQRNS. In this work, the filter structure is extended for non-uniformly spaced frequency samples and has been termed the generalized number theoretic filter structure. It is shown that for the implementation of this generalized structure, the MQRNS is more efficient than the conventional RNS; the QRNS does not support appropriate fields for the generalized structure.Dept. of Electrical and Computer Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1985 .K757. Source: Dissertation Abstracts International, Volume: 46-08, Section: B, page: 2757. Thesis (Ph.D.)--University of Windsor (Canada), 1985

    Design of doubly-complementary IIR digital filters using a single complex allpass filter, with multirate applications

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    It is shown that a large class of real-coefficient doubly-complementary IIR transfer function pairs can be implemented by means of a single complex allpass filter. For a real input sequence, the real part of the output sequence corresponds to the output of one of the transfer functions G(z) (for example, lowpass), whereas the imaginary part of the output sequence corresponds to its "complementary" filter H(z)(for example, highpass). The resulting implementation is structurally lossless, and hence the implementations of G(z) and H(z) have very low passband sensitivity. Numerical design examples are included, and a typical numerical example shows that the new implementation with 4 bits per multiplier is considerably better than a direct form implementation with 9 bits per multiplier. Multirate filter bank applications (quadrature mirror filtering) are outlined

    Circulant and skew-circulant matrices as new normal-form realization of IIR digital filters

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    Normal-form fixed-point state-space realization of IIR (infinite-impulse response) filters are known to be free from both overflow oscillations and roundoff limit cycles, provided magnitude truncation arithmetic is used together with two's-complement overflow features. Two normal-form realizations are derived that utilize circulant and skew-circulant matrices as their state transition matrices. The advantage of these realizations is that the A-matrix has only N (rather than N2) distinct elements and is amenable to efficient memory-oriented implementation. The problem of scaling the internal signals in these structures is addressed, and it is shown that an approximate solution can be obtained through a numerical optimization method. Several numerical examples are included

    Low passband sensitivity digital filters: A generalized viewpoint and synthesis procedures

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    The concepts of losslessness and maximum available power are basic to the low-sensitivity properties of doubly terminated lossless networks of the continuous-time domain. Based on similar concepts, we develop a new theory for low-sensitivity discrete-time filter structures. The mathematical setup for the development is the bounded-real property of transfer functions and matrices. Starting from this property, we derive procedures for the synthesis of any stable digital filter transfer function by means of a low-sensitivity structure. Most of the structures generated by this approach are interconnections of a basic building block called digital "two-pair," and each two-pair is characterized by a lossless bounded-real (LBR) transfer matrix. The theory and synthesis procedures also cover special cases such as wave digital filters, which are derived from continuous-time networks, and digital lattice structures, which are closely related to unit elements of distributed network theory

    Tree-structured complementary filter banks using all-pass sections

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    Tree-structured complementary filter banks are developed with transfer functions that are simultaneously all-pass complementary and power complementary. Using a formulation based on unitary transforms and all-pass functions, we obtain analysis and synthesis filter banks which are related through a transposition operation, such that the cascade of analysis and synthesis filter banks achieves an all-pass function. The simplest structure is obtained using a Hadamard transform, which is shown to correspond to a binary tree structure. Tree structures can be generated for a variety of other unitary transforms as well. In addition, given a tree-structured filter bank where the number of bands is a power of two, simple methods are developed to generate complementary filter banks with an arbitrary number of channels, which retain the transpose relationship between analysis and synthesis banks, and allow for any combination of bandwidths. The structural properties of the filter banks are illustrated with design examples, and multirate applications are outlined

    On error-spectrum shaping in state-space digital filters

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    A new scheme for shaping the error spectrum in state-space digital filter structures is proposed. The scheme is based on the application of diagonal second-order error feedback, and can be used in any arbitrary state-space structure having arbitrary order. A method to obtain noise-optimal state-space structures for fixed error feedback coefficients, starting from noise optimal structures in absence of error feedback (the Mullis and Roberts Structures), is also outlined. This optimization is based on the theory of continuous equivalence for state-space structures

    Minimal structures for the implementation of digital rational lossless systems

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    Digital lossless transfer matrices and vectors (power-complementary vectors) are discussed for applications in digital filter bank systems, both single rate and multirate. Two structures for the implementation of rational lossless systems are presented. The first structure represents a characterization of single-input, multioutput lossless systems in terms of complex planar rotations, whereas the second structure offers a representation of M-input, M-output lossless systems in terms of unit-norm vectors. This property makes the second structure desirable in applications that involve optimization of the parameters. Modifications of the second structure for implementing single-input, multioutput, and lossless bounded real (LBR) systems are also included. The main importance of the structures is that they are completely general, i.e. they span the entire set of M×1 and M×M lossless systems. This is demonstrated by showing that any such system can be synthesized using these structures. The structures are also minimal in the sense that they use the smallest number of scalar delays and parameters to implement a lossless system of given degree and dimensions. A design example to demonstrate the main results is included

    Digital filter design using root moments for sum-of-all-pass structures from complete and partial specifications

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    Passive cascaded-lattice structures for low-sensitivity FIR filter design, with applications to filter banks

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    A class of nonrecursive cascaded-lattice structures is derived, for the implementation of finite-impulse response (FIR) digital filters. The building blocks are lossless and the transfer function can be implemented as a sequence of planar rotations. The structures can be used for the synthesis of any scalar FIR transfer function H(z) with no restriction on the location of zeros; at the same time, all the lattice coefficients have magnitude bounded above by unity. The structures have excellent passband sensitivity because of inherent passivity, and are automatically internally scaled, in an L_2 sense. The ideas are also extended for the realization of a bank of MFIR transfer functions as a cascaded lattice. Applications of these structures in subband coding and in multirate signal processing are outlined. Numerical design examples are included
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